Simplify the following: (x2+x-6)/(x2+7x+12) x (x-2)/(x(x+4))

May 14, 2026Mathematics

ScanSolve AI Answer

May 14, 2026

Answer

$\frac{(x-2)^2}{x(x+4)^2}$

Here is the solution to the question:

2.2.3. Simplify the following: $\frac{x^2+x-6}{x^2+7x+12} \times \frac{x-2}{x(x+4)}$ Step 1: Factorize the quadratic expressions in the first fraction. The numerator $x^2+x-6$ factors into $(x+3)(x-2)$ . The denominator $x^2+7x+12$ factors into $(x+3)(x+4)$ . Substitute these factored forms back into the expression: $\frac{(x+3)(x-2)}{(x+3)(x+4)} \times \frac{x-2}{x(x+4)}$ Step 2: Cancel out the common factor $(x+3)$ from the first fraction, assuming $x \neq -3$ . $\frac{x-2}{x+4} \times \frac{x-2}{x(x+4)}$ Step 3: Multiply the numerators and the denominators. $\frac{(x-2)(x-2)}{(x+4)x(x+4)}$ $\frac{(x-2)^2}{x(x+4)^2}$ The simplified expression is $\boxed{\frac{(x-2)^2}{x(x+4)^2}}$ .

Drop the next question.

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

Qएक अध्यापक किसी खान कूपक में 6m प्रति मिनट की दर से नीचे जाता है। यदि नीचे जाना प्रारंभ तल से 10 m ऊ…Qमोहिनी टेस्ट में (-5) अंक प्राप्त करती है, जबकि उसको 7 उत्तर सही पाने के लिए 20 अंक मिलते हैं। उसने…QFind the local time of Yanga in Tanzania, which is located at longitude 39° East, if it is 12:00 noo…QCacheprobe1780603963316: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.QCacheprobe1780603930644: A cyclist rides 90 km in 2 hours. Average speed in km/h? Show work.

See all Mathematics questions →

Still have questions?

Quick Answer

2.2.3. Simplify the following: (x^2+x-6)/(x^2+7x+12) × (x-2)/(x(x+4)) Step 1: Factorize the quadratic expressions in the first fraction.

Asked on May 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 14, 2026

Here is the solution to the question: 2.2.3. Simplify the following: (x^2+x-6)/(x^2+7x+12) × (x-2)/(x(x+4)) Step 1: Factorize the quadratic expressions in the first fraction. The numerator x^2+x-6 factors into (x+3)(x-2). The denominator x^2+7x+12 factors into (x+3)(x+4). Substitute these factored forms back into the expression: ((x+3)(x-2))/((x+3)(x+4)) × (x-2)/(x(x+4)) Step 2: Cancel out the common factor (x+3) from the first fraction, assuming x ≠ -3. (x-2)/(x+4) × (x-2)/(x(x+4)) Step 3: Multiply the numerators and the denominators. ((x-2)(x-2))/((x+4)x(x+4)) ((x-2)^2)/(x(x+4)^2) The simplified expression is ((x-2)^2)/(x(x+4)^2). Drop the next question.